Page "Complemented lattice" ¶ 4
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## Some Related Sentences

Every and complemented
Every Saturday, a wide variety of producers from around the country take part in the very popular market selling quality produce including a huge array of hot foods, complemented by many others selling hand-made jewellery, gifts, childrenswear and vintage clothing.

Every and distributive
Every Boolean algebra is a Heyting algebra when a → b is defined as usual as ¬ a ∨ b, as is every complete distributive lattice when a → b is taken to be the supremum of the set of all c for which a ∧ c ≤ b. The open sets of a topological space form a complete distributive lattice and hence a Heyting algebra.
* Every Boolean algebra is a distributive lattice.
* Every Heyting algebra is a distributive lattice.
* Every totally ordered set is a distributive lattice with max as join and min as meet.
Every distributive lattice is modular.

Every and lattice
Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.
* Every totally ordered set that is a bounded lattice is also a Heyting algebra, where is equal to when, and 1 otherwise.
Every complete lattice is also a bounded lattice, which is to say that it has a greatest and least element.
Every lattice in can be generated from a basis for the vector space by forming all linear combinations with integer coefficients.
* Every substructure is the union of its finitely generated substructures ; hence Sub ( A ) is an algebraic lattice.
Also, a kind of converse holds: Every algebraic lattice is isomorphic to Sub ( A ) for some algebra A.
Every non-modular lattice contains a copy of N < sub > 5 </ sub > as a sublattice.
Every quasinormal subgroup is a modular subgroup, that is, a modular element in the lattice of subgroups.

Every and has
Every soldier in the army has, somewhere, relatives who are close to starvation.
Every woman has had the experience of saying no when she meant yes, and saying yes when she meant no.
Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.
Every calculation has been made independently by two workers and checked by one of the editors.
Every retiring person has a different situation facing him.
Every family of Riviera Presbyterian Church has been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project in which all members of the family participate.
Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.
`` Every woman in the block has tried that ''.
: Every set has a choice function.
Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set.
** Every surjective function has a right inverse.
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
** Antichain principle: Every partially ordered set has a maximal antichain.
** Every vector space has a basis.
* Every small category has a skeleton.
* Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).
** Every field has an algebraic closure.
** Every field extension has a transcendence basis.
** Every Tychonoff space has a Stone – Čech compactification.
* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =
Every unit of length has a corresponding unit of area, namely the area of a square with the given side length.
Every field has an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of choice.
Every ATM cell has an 8-or 12-bit Virtual Path Identifier ( VPI ) and 16-bit Virtual Channel Identifier ( VCI ) pair defined in its header.

Every and unique
Every real number, whether integer, rational, or irrational, has a unique location on the line.
Every other aspect of film making originated in a different medium than film ( photography, art direction, writing, sound recording ), but editing is the one process that is unique to film.
Every rational number has a unique representation as an irreducible fraction.
Every species can be given a unique ( and, one hopes, stable ) name, as compared with common names that are often neither unique nor consistent from place to place and language to language.
Every LORAN chain in the world uses a unique Group Repetition Interval, the number of which, when multiplied by ten, gives how many microseconds pass between pulses from a given station in the chain.
Every principal ideal domain is a unique factorization domain ( UFD ).
Every pair of points belongs to a unique line.
Every non-negative real number a has a unique non-negative square root, called the principal square root, which is denoted by, where √ is called the radical sign or radix.
Every element s, except a possible greatest element, has a unique successor ( next element ), namely the least element of the subset of all elements greater than s. Every subset which has an upper bound has a least upper bound.
Every well-ordered set is uniquely order isomorphic to a unique ordinal number, called the order type of the well-ordered set.
# Every noun belongs to a unique number class.
* Every rational number has an essentially unique continued fraction representation.
Every system is unique to the business drivers it supports, therefore the quality attributes of each system such as fault-tolerance, backward compatibility, extensibility, reliability, maintainability, availability, security, usability, and such other – ilities will vary with each implementation.
Every Gundam has a unique name that befits the nature of the suit and / or its origins, such as the XXXG-01W Wing Gundam, XXXG-01D Gundam Deathscythe and the XXXG-01S Shenlong Gundam.
* PASSIA Diaries and Annual Reports: Every year since 1988, PASSIA publishes its “ Diary ”, a unique annual resource book combining a comprehensive directory of contact information for Palestinian and interna tional institu tions operating in Palestine, a day-to-day calendar, and an agenda containing facts and figures, graphs, statistics, chronologies and maps related to Palestine and the Palestinians.
Every composite number can be written as the product of two or more ( not necessarily distinct ) primes ; furthermore, this representation is unique up to the order of the factors.
: Every host in the network must have a unique address that determines where it is.
Every crystalline solid will have a unique pattern of d-spacings ( known as the powder pattern ), which is a “ finger print ” for that solid.
One unique challenge that the team encountered early on was related to deph perception, the team remedied through the use of shadows: Every object in the game has a shadow directly below it regardless of the area's lighting.
Every June this area is inundated with the Ronceverte River Festival, where a unique raffle is held by floating hundreds of small, numbered yellow ducks into the river.
Every device on the bus has a unique 5-bit primary address, in the range from 0 to 30 ( 31 total possible addresses ).
Every unique cultivar has a unique name within its denomination class ( which is almost always the genus ).

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